Honda Recon shut of while driving and now won’t start

welcome to the site
NOW< some more info
how often do you use this atv, does it sit a LOT

if it sits a lot, its very possible your fuel is BAD, ethanol fuel can go bad in a few weeks
so,

maybe start with draining the tank, make sure its clean inside too when drained
then check and make sure your fuel peacock is working and flowing well

NEXT< if it was me I would replace fuel line from tank to carb, cheap easy way to know fuel line is clean and not varnish coated!
THEN< its time to clean your carb, as sounds like you have a fuel supply issue, and by cleaning tank, peacock,line and now carb, then starting with new fuel,
you rule out all these issues as possible causes to your problem!
and most likely will resolve your issue in the process

also, if this atv sits often, I HIGHLY suggest buying NON ethanol fuel for use in and and TREAT IT as well!

pressure washing can be very bad on atv's
yes it sure removes mud and junk, but it also forces water into places it shouldn;t be
and can ruin bearings and seals

if these issues started after power washing, I'm guessing you got water in an electrical connection and is causing you issue's
I would check all connections and even clean and dielectric coat all connections, start with spark plug cap, fuses, and then CDI and other major power points, and keep going till you find the one!

I will again say I would never rule out fuel, you can BUY bad fuel, so it doesn;t have to be fuel sitting about a long time for it to go bad, can also be bad from the get go, just a tad too much water in it or mixed with older fuel at station and BOOM you have NEW issue's

but this sounds more like a power washer issue,
and you just got some electrical part wet that should have!

Maybe even pull your CDI and pout it in a baggie full of dry rice for a day or so, or place out in the sun to dry insides better!